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Ramsey theory over partitions very good scale Constructible Universe Minimal Walks Distributive tree Ulam matrix Poset O-space HOD 54G20 Successor of Regular Cardinal incompactness nonmeager set Sakurai's Bell inequality Foundations Greatly Mahlo projective Boolean algebra Rainbow sets middle diamond Prevalent singular cardinals Forcing Coherent tree free Boolean algebra Closed coloring indecomposable ultrafilter Chromatic number Successor of Singular Cardinal Absoluteness Hereditarily Lindelöf space regressive Souslin tree PFA(S)[S] Uniformization Fodor-type reflection stationary hitting specializable Souslin tree Shelah's Strong Hypothesis Reflecting stationary set Almost Souslin Aronszajn tree coloring number weak square Prikry-type forcing ZFC construction Postprocessing function Fat stationary set Singular Density S-Space Generalized descriptive set theory Forcing Axioms Dowker space Vanishing levels free Souslin tree Souslin Tree countably metacompact transformations Kurepa Hypothesis Mandelbrot set PFA Luzin set approachability ideal Microscopic Approach polarized partition relation Was Ulam right unbounded function Generalized Clubs tensor product graph Erdos Cardinal club_AD Square-Brackets Partition Relations Analytic sets Cardinal function C-sequence diamond star weak diamond Chang's conjecture Dushnik-Miller Diamond Open Access Rock n' Roll Axiom R Amenable C-sequence Well-behaved magma Large Cardinals SNR Martin's Axiom Precaliber Subtle tree property Club Guessing P-Ideal Dichotomy Subtle cardinal full tree Knaster Filter reflection Diamond-sharp Sierpinski's onto mapping principle OCA Jonsson cardinal b-scale super-Souslin tree Ineffable cardinal Slim tree Hedetniemi's conjecture Local Club Condensation. positive partition relation Singular cofinality Hindman's Theorem Cohen real AIM forcing square Diamond for trees xbox Rado's conjecture Small forcing Almost-disjoint family square principles Knaster and friends Antichain Ostaszewski square Strong coloring Strongly Luzin set reflection principles GMA higher Baire space stationary reflection ccc Cardinal Invariants Whitehead Problem Reduced Power Commutative cancellative semigroups Subadditive Partition Relations sap Singular cardinals combinatorics Almost countably chromatic Universal Sequences Uniformly homogeneous Erdos-Hajnal graphs Nonspecial tree strongly bounded groups Uniformly coherent Ascent Path Weakly compact cardinal Iterated forcing Sigma-Prikry Non-saturation Parameterized proxy principle Lipschitz reduction stick Fast club Selective Ultrafilter Subnormal ideal L-space
Blog Archives
The eightfold way
Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. Three central combinatorial properties in set theory are the tree property, the approachability property and stationary reflection. We prove the mutual independence of these properties by showing … Continue reading
Ordinal definable subsets of singular cardinals
Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. A remarkable result by Shelah states that if $\kappa$ is a singular strong limit cardinal of uncountable cofinality then there is a subset $x$ of $\kappa$ such … Continue reading
Posted in Publications, Singular Cardinals Combinatorics
Tagged AIM forcing, HOD, Singular cardinals combinatorics
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